The effect of grid quality and weight derivatives in density functional calculations of harmonic vibrational frequencies

We investigate the accuracy of harmonic vibrational frequencies computed with and without the inclusion of quadrature weight derivatives in our recently completed initial implementation of density functional theory (DFT) analytical second derivatives. Unlike the situation with analytical DFT gradients, second derivatives are much more sensitive to the inclusion of weight derivatives, and omitting them can produce nonsensical results unless the numerical grid is of sufficiently high quality. Results are presented for the homonuclear diatomics F2, Cl2, Br2, and I2 and for a number of larger molecules. Errors introduced by excluding weight derivatives increase with increasing atomic number and increasing basis set size. The origin of the error is the difficulty of accurately integrating high-order derivatives of basis functions with large exponents around their own atomic center, and it is not the weight derivatives themselves that eliminate this error but the fact that proper allowance for atom-centered gri...

[1]  W. Kohn,et al.  Self-Consistent Equations Including Exchange and Correlation Effects , 1965 .

[2]  J. Pople,et al.  Self‐Consistent Molecular Orbital Methods. IV. Use of Gaussian Expansions of Slater‐Type Orbitals. Extension to Second‐Row Molecules , 1970 .

[3]  A. Wachters,et al.  Gaussian Basis Set for Molecular Wavefunctions Containing Third‐Row Atoms , 1970 .

[4]  Mark S. Gordon,et al.  Self-consistent molecular-orbital methods. 22. Small split-valence basis sets for second-row elements , 1980 .

[5]  E. Baerends,et al.  The calculation of interaction energies using the pseudopotential Hartree–Fock–Slater–LCAO method , 1984 .

[6]  A. Becke A multicenter numerical integration scheme for polyatomic molecules , 1988 .

[7]  R. Parr Density-functional theory of atoms and molecules , 1989 .

[8]  B. Delley An all‐electron numerical method for solving the local density functional for polyatomic molecules , 1990 .

[9]  D. Salahub,et al.  New algorithm for the optimization of geometries in local density functional theory , 1990 .

[10]  Jan K. Labanowski,et al.  Density Functional Methods in Chemistry , 1991 .

[11]  Dennis R. Salahub,et al.  Optimization of Gaussian-type basis sets for local spin density functional calculations. Part I. Boron through neon, optimization technique and validation , 1992 .

[12]  A. Becke Density-functional thermochemistry. III. The role of exact exchange , 1993 .

[13]  Nicholas C. Handy,et al.  Analytic Second Derivatives of the Potential Energy Surface , 1993 .

[14]  Benny G. Johnson,et al.  The performance of a family of density functional methods , 1993 .

[15]  C. W. Murray,et al.  Quadrature schemes for integrals of density functional theory , 1993 .

[16]  Andrew Komornicki,et al.  Molecular gradients and hessians implemented in density functional theory , 1993 .

[17]  Benny G. Johnson,et al.  An implementation of analytic second derivatives of the gradient‐corrected density functional energy , 1994 .

[18]  Jon Baker,et al.  The effect of grid quality and weight derivatives in density functional calculations , 1994 .

[19]  R. Ahlrichs,et al.  Efficient molecular numerical integration schemes , 1995 .

[20]  Jon Baker,et al.  Molecular energies and properties from density functional theory: Exploring basis set dependence of Kohn—Sham equation using several density functionals , 1997 .

[21]  N. Handy,et al.  Left-right correlation energy , 2001 .

[22]  Filipp Furche,et al.  An efficient implementation of second analytical derivatives for density functional methods , 2002 .

[23]  P. Pulay,et al.  An improved 6-31G* basis set for first-row transition metals , 2003 .